Here is the full list of all 37 Rebel Galaxy achievements. It takes around 50-60 hours to unlock all of the achievements on Windows.
Hack 10 transponders successfully
Destroy 2,500 Fighter-Class Craft
Destroy 1,000 Capital-Class Craft
Shoot down 500 torpedoes
Complete 50 missions from the mission board
Salvage 50 Containers
Pirate a merchant
Mine 50 asteroids using a Fault Tracker
Collect 100 bounties
Kill 1 Pirate Lord
Kill 20 Pirate Lords
Reach rank 5 in any Guild
Find the Face of Gozu
Find an Antimatter Speck
Break 1 blockade
Break 10 blockades
Find a Progenitor Shard
Gather 200 objects with a tractor beam
Complete the main campaign
Rescue 20 merchants
Become neutral to pirate factions
Join the Mercenaries' Guild
Successfully bribe a Militia official
Purchase a Dreadnaught-class ship
Jump out of the first solar system
Destroy 100 Capital-Class Craft
Destroy 250 Fighter-Class Craft
Hire a mercenary
Become friendly to the Militia
Reach a Net Worth of 50 Million Credits
Purchase a Destroyer-class ship
Reach a Net Worth of 5 Million Credits
Collect 10 bounties
Join the Merchant's Guild
Purchase a new ship
Woke Trell
Trade with a Merchant while in flight